First the bad news. 5e does not seem to have a Ring of Sustenance like the earlier editions of D&D, and a Bead of Nourishment isn't going to help you if you can't get it in their mouth somehow. There are also no spells that can really help, there's no way to get a Goodberry inside the character's mouth. You might try to argue that a stomach is a container, but then Create Food and Water might instantly kill the character because it creates 45 gallons worth of food, which seems a bit excessive.
Instead, try to get rid of the magical thread so they can eat the normal way again.
The character had their mouth sewn shut by magical thread they can't cut, so cut around the magical thread and then figure out later how you're going to fix the poor Tortle's face later. Better to be a reptilian Joker than to starve to death. Alternatively, you could try making a hole in their cheek to insert food through, if the thread won't sew that shut, it might be the less severe, but less 'complete' solution.
Alternatively, see if you can nullify the magic of the thread. Perhaps there's a Dead Magic Zone that will do the trick or you can find somebody to cast anti-magic zone, or perhaps the DM will be generous and agree that the wire itself is mundane and the magic keeping it from being cut is a spell cast on it, in which case Dispel Magic might work.
If that also doesn't work, there might be more drastic ways to keep the character from starving to death, such as using a spell or a monster to turn them to stone. A different, higher level solution would be to True Polymorph the character into a creature that doesn't need to eat, such as an undead or a construct. You could also use any of the other higher level spells that remove the need to eat: Sequester, Imprisonment or astral projection.